Syllabus

Module 1: (8 hours)
Green’s theorem, Method of Green’s function, Solution to boundary value problems using method of images and Green's functions technique, Green's reciprocation theorem, Green's Functions in Spherical Coordinates.

Module 2: (6 hours)
Poynting theorem and energy conservation by EM fields, Maxwell's stress tensor and momentum conservation with examples.

Module 3: (14 hours)
Electromagnetic (EM) waves in vacuum, Energy and momentum in EM waves, Boundary conditions for EM waves in matter, Reflection and transmission of EM waves, EM waves in conductors and dielectrics, Normal and anomalous dispersion, Causality and the Kramers-Kronig relations.

Module 4: (6 hours)
Waveguides, Boundary conditions, Rectangular and circular waveguides, TE, TM and TEM modes, Coaxial cables.

Module 5: (4 hours)
Potential formulation: Scalar and Vector Potential, Gauge invariance, Coulomb gauge and Lorentz gauge, Retarded potentials.

Module 6: (8 hours)
Electric field in different reference frames, Radiation from a point charge, Radiation from electric and magnetic dipoles, Radiation reaction, Radiation damping.

To learn the principles of electrodynamics and to apply Maxwell’s equations for calculating the electric and magnetic fields.

To learn to solve boundary value problems involving electric and magnetic fields.

To understand how energy and momenta are conserved by the EM fields.

To understand the principles of EM wave transmission through different media and waveguides.

5. To learn about the radiation from moving charges and oscillating dipoles.

At the end of the course, students will be able to:
CO1: Write down the fundamental equations governing the behavior of EM fields in bulk and the boundary conditions at the interface.

CO2: Explain how energy and momenta are conserved by EM fields.

CO3: Apply those equations to characterize the propagation of EM waves through different types of media.

CO4: Apply Green’s function method to solve boundary value problems.

CO5: Examine the characteristics of EM radiation by point charges and dipoles.

D. J. Griffiths, Introduction to Electrodynamics, Cambridge University Press , 4th Edition (2020).

A. Zangwill, Modern Electrodynamics, Cambridge University Press , 1st Edition (2012).

J. D. Jackson, Classical Electrodynamics, Wiley , 3rd Edition (2007).

D. J. Morin and E. M. Purcell, Electricity and Magnetism, Cambridge University Press , 3rd Edition (2013).